Models

Unrestricted case (φ ≠ 0) or restricted case (φ = 0)

Coefficient Driver of Equation (4)

Coefficient Estimates of γ_0t in Equations (3) and (4)

Coefficient Driver of Equation (5)

Coefficient Estimates of γ_1t in Equations (3) and (5)

Theil Forecasting Values

Conclusion

Z_it

π₀₀

π_0i

Z_jt

π₁₀

π_1j

U Statistic

Accept/Reject

II

φ = 0

CEXPI

33584.40

157.36

II

14.24

−0.00054

0.67

REJECT

(4.540)^a

(3.267)^a

(9.580)^a

(−5.803)^a

III

φ = 0

OMT

10646.68

457.72

II

10.78

−0.00038

0.53

REJECT

(1.383)

(6.128)^a

(8.625)^a

(−4.975)^a

IV

φ = 0

REEXR

124224.59

−560.23

II

12.679

−0.00047

0.69

REJECT

(4.635)^a

(−2.491)^b

(8.362)^a

(−4.941)^a

V

φ ≠ 0

CEXPI

99318.03

−183.48

IM

3.73

−0.00011

0.33

ACCEPT

(12.24)^a

(−3.266)^a

(6.916)^a

(−2.063)^b

VI

φ = 0

CEXPI

132794.50

−390.82

IM

3.569

−0.00015

2.38

REJECT

(13.11)^a

(−4.948)^a

(13.59)^a

(−6.231)^a

VII

φ ≠ 0

OMT

70503.24

58.56

IM

4.476

−0.00013

0.39

REJECT

(5.594)^a

(0.520)

(6.905)^a

(−2.120)^b

VIII

φ = 0

OMT

10195.42

641.03

IM

3.894

−0.00017

1.77

REJECT

(0.6130)

(4.493)^a

(15.30)^a

(−6.956)^a

IX

φ = 0

REEXR

174796.17

−773.52

IM

3.901

−0.00017

2.18

REJECT

(5.634)^a

(−2.921)^a

(14.14)^a

(−6.707)^a

X

φ = 0

CEXPI

34662.15

152.99

RCREI

13.18

−0.0003

7.15

REJECT

(4.512)^a

(3.054)^a

(9.078)^a

(−5.244)^a

XI

φ = 0

OMT

9875.12

468.13

RCREI

9.99

−0.00021

5.17

REJECT

(1.247)

(6.010)^a

(8.293)^a

(−4.537)^a

XII

φ = 0

REEXR

125398.15

−566.97

RCREI

11.75

−0.00026

6.41

REJECT

(4.539)^a

(−2.446)^b

(8.010)^a

(−4.499)^a